Class 12

Math

3D Geometry

Three Dimensional Geometry

Find the equation of the plane which contains two parallel lines given by $1x−3 =−4y+2 =5z $ and $1x−4 =−4y−3 =5z−2 $.

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

Find the equation of the plane passing through the point $(−1,3,2)$ and perpendicular to each of the planes $x+2y+3z=5and3x+3y+z=0.$

Shortest distance between the lines $1x−1 =1y−1 =1z−1 and1x−2 =1y−3 =1z−4 $ is equal to a. $14 $ b. $7 $ c. $2 $ d. none of these

The equation of the plane through the intersection of the planes $x+2y+3z−4=0and4x+3y+2z+1=0$ and passing through the origin is (a) $17x+14y+11z=0$ (b) $7x+4y+z=0$ (c) $x+14+11z=0$ (d) $17x+y+z=0$

Show that $ax+by+r=0,by+cz+p=0andcz+ax+q=0$ are perpendicular to $x−y,y−zandz−x$ planes, respectively.

Find the equations of the bisectors of the angles between the planes $2x−y+2z+3=0and3x−2y+6z+8=0$ and specify the plane which bisects the acute angle and the plane which bisects the obtuse angle.

If $A(3,2,−4),B(5,4,−6)andC(9,8,−10)$ are three collinear points, then find the ratio in which point $C$ divides $AB˙$

Find the distance between the parallel planes $x+2y−2z+1=0and2x+4y−4z+5=0.$

The point of intersection of the line passing through $(0,0,1)$ and intersecting the lines $x+2y+z=1,−x+y−2z=2$ and $x+y=2,x+z=2$ with $xy$ plane is a. $(35 ,−31 ,0)$ b. $(1,1,0)$ c. $(32 ,31 ,0)$ d. $(−35 ,31 ,0)$